Example of O(n!)?

Question

What is an example (in code) of a O(n!) function? It should take appropriate number of operations to run in reference to n; that is, I\'m asking a

Answer 1

You are right the recursive calls should take exactly n! time. here is a code like to test factorial time for n different values. Inner loop runs for n! time for different values of j, so the complexity of inner loop is Big O(n!)

public static void NFactorialRuntime(int n)
    {
        Console.WriteLine(" N   Fn   N!");
        for (int i = 1; i <= n; i++)  // This loop is just to test n different values
        {
            int f = Fact(i);
            for (int j = 1; j <= f; j++)  // This is Factorial times
            {  ++x; }
            Console.WriteLine(" {0}   {1}   {2}", i, x, f);
            x = 0;
        }
    }

Here are the test result for n = 5, it iterate exactly factorial time.

  N   Fn   N!
  1   1   1
  2   2   2
  3   6   6
  4   24   24
  5   120   120

Exact function with time complexity n!

// Big O(n!)
public static void NFactorialRuntime(int n)
    {
        for (int j = 1; j <= Fact(i); j++) {  ++x; }
        Console.WriteLine(" {0}   {1}   {2}", i, x, f);
    }